Superconductivity and
Low Temperature Physics II
Lecture Notes Summer Semester 2013
R. Gross and A. Marx
© Walther-Meißner-Institute
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General Remarks on the Courses to the Field
Superconductivity and Low Temperature Physics
The following lectures are offered on a regular basis: 1. Superconductivity and Low Temperature Physics I
Foundations of Superconductivity
2. Superconductivity and Low Temperature Physics II (SS 2013: Thu., 12:30h, HS 3) Foundations of Low Temperature Physics and Techniques
3. Applied Superconductivity (SS 2013: Mon. & Wed., 14:15h, WMI) Josephson-Effects, Superconducting Electronics, Quantum Circuits
4. Several Seminars (see announcements)
Documents and Hints: http://www.wmi.badw.de Teaching (announcement of lectures) Lecture Notes (download of scripts, handouts, etc.)
Seminars (announcement of seminars)
SS 2013: - Advances in Solid-State Physics Tue. 10:15 – 11:30h Seminar room 143, WMI - Superconducting Quantum Circuits Tue. 14:30 – 16:00h Library, WMI
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Applied Superconductivity Superconductivity and Low Temperature Physics II
Spin Electronics
Sum
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Sem
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3
VO, ÜB,
Skript
Seminar: Superconducting Quantum Circuits
Tue., 14.30 – 16.00 h, Seminar room, WMI
Seminar: Advances in Solid State Physics
Tue., 10.15 – 11.45 h, Seminar room, WMI
Seminar: Spin Mechanics and Spin Dynamics
Wed., 10.15 – 11.45 h Seminar room, WMI
Mon. and Wed., 14.15 – 15.45 h Seminar room, WMI
Tue, 13.30 – 15.00 h Seminar room, WMI
VO, ÜB,
Skript
VO, ÜB,
Skript
Rudolf Gross Frank Deppe
Thu, 12.30 – 14.00 h Physics Department, HS3
Hans Hübl
S. Gönnenwein
Walther-Meißner-Institut (www.wmi.badw.de)
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year name discovery
1913 Heike Kamerlingh Onnes "For his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium"
1972 John Bardeen, Leon Neil Cooper und Robert Schrieffer
"for their jointly developed theory of superconductivity, usually called the BCS-theory"
1973 Brian David Josephson "for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effect"
1978 Pjotr Kapiza "for his basic inventions and discoveries in the area of low-temperature physics"
1985 Klaus von Klitzing "for the discovery of the quantized Hall effect"
1987 Johannes Georg Bednorz und Karl Alex Müller
"for their important break-through in the discovery of superconductivity in ceramic materials"
1996 David M. Lee, Douglas D. Osheroff und Robert C. Richardson
"for their discovery of superfluidity in helium-3"
1997 Steven Chu, Claude Cohen-Tannoudji und William D. Phillips
"for development of methods to cool and trap atoms with laser light" See Laser cooling.
1998 Robert B. Laughlin, Horst Ludwig Störmer und Daniel Chee Tsui
"for their discovery of a new form of quantum fluid with fractionally charged excitations". See Quantum Hall effect.
2001 Eric A. Cornell, Wolfgang Ketterle und Carl E. Wieman
"for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates"
2003 Alexei Abrikosov, Witali Ginsburg und Anthony James Leggett
"for pioneering contributions to the theory of superconductors and superfluids"
Nobel Prizes in Physics related to low temperature physics
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Superconductivity and
Low Temperature Physics II
Contents of the Lecture
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I.1 Foundations and General Properties I.1.1 Quantum Fluids I.1.2 Helium I.1.3 Van der Waals Bonding I.1.4 Zero-Point Fluctuations I.1.5 Helium under Pressure I.1.6 pT-Phase Diagram of 4He and 3He I.1.7 Characteristic Properties of 4He and 3He I.1.8 Specific Heat of 4He and 3He
I.2 4He as an Ideal Bose Gas I.2.1 Bose-Einstein Condensation I.2.2 Bose-Einstein Condensation of 4He
I.3 Superfluid 4He I.3.1 Experimental Observations I.3.2 Two-Fluid Model I.3.3 Excitation Spectrum of 4He
I.4 Vortices I.4.1 Quantization of Circulation I.4.2 Experimental Study of Vortices
Contents Part I: Quantum Fluids
I.5 3He I.5.1 normal fluid 3He I.5.2 solid 3He and Pomeranchuk effect I.5.3 superfluid 3He I.6 3He / 4He mixtures
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II.1 Specific Heat II.1.1
II.2 Thermal Conductance II.2.1
II.3 Phonons and Electrons II.3.1
II.4 Magnetic Moments II.4.1
Contents Part II: Solids at Low Temperature
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III.1 Introduction III.1.1 General Remarks III.1.2 Mesoscopic Systems III.1.3 Characteristic Length Scales III.1.4 Characteristic Energy Scales III.1.5 Transport Regimes
III.2 Description of Electron Transport by Scattering of Waves III.2.1 Electron Waves and Waveguides III.2.2 Landauer Formalism III.2.3 Multi-terminal Conductors
III.3 Quantum Interference Effects III.3.1 Double Slit Experiment III.3.2 Two Barriers – Resonant Tunneling III.3.3 Aharonov-Bohm Effect III.3.4 Weak Localization III.3.5 Universal Conductance Fluctuations
III.4 From Quantum Mechanics to Ohm‘s Law
III.5 Coulomb Blockade
Contents Part III: Quantum Transport in Nanostructures
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IV.1 Generation of Low Temperatures IV.1.1 Introduction IV.1.2 Expansion Machine IV.1.3 Regenerative Machine IV.1.4 Joule-Thomson Cooling IV.1.5 Summary IV.1.6 Evaporation Cooling IV.1.7 Dilution Cooling IV.1.8 Pomeranchuk Cooling IV.1.9 Adiabatic Demagnetization
IV.2 Thermometry IV.2.1 Introduction IV.2.2 Primary Thermometers IV.2.3 Secondary Thermometers
Contents Part IV: Cryogenic Techniques:
Generation and Measurement of LT
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• F. Pobell Matter and Methods at Low Temperatures, Springer 1996
• D.R. Tilley and J. Tilley Superfluidity and Superconductivity, Adam Hilger 1990
• C. Enss and S. Hunklinger Low-Temperature Physics, Springer 2005
• P.V.E. McClintock, D.J. Meredith, J.K. Wigmore Matter at Low Temperatures, Blackie 1984
• J. Wilks, D.S. Betts Introduction to Liquid Helium, Oxford 1987
• A. Kent Experimental Low Temperarure Physics, MacMillan, New York
• G.K. White, P.J. Meeson Experimental Techniques in Low Temperature Physics Oxford University Press, 2002
• K.H. Bennemann, J.B. Ketterson The Physics of Liquid and Solid Helium I and II, Wiley 1978
• H. Frey, R.A. Haefer Tieftemperaturtechnologie, VDI-Verlag, Düsseldorf 1981
• Yoseph Imry Introduction to Mesoscopic Physics Oxford University Press, Oxford (1997)
• Supriyoto Datta Electronic Transport in Mesoscopic Systems Cambridge University Press, Cambridge (1995)
• Thomas Heinzel Mesoscopic Electronic in Solid State Nanostructures Wiley VCH, Weinheim (2003)
Literature
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•magnetism
•mesoscopic physics
•nanoscale superconducting and spintronic devices
•superconducting quantum bits
•………
an appetizer
Low Temperature Physics at WMI
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25 nm
Nb Au
Flux Qubit WMI
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Pr1.85Ce0.15CuO4
Crystal Growth Lab
YBa2Cu3O7-d
Bi2Sr2CaCu2O8+d Image Furnace
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fiber for IR laser heating
substrate manipulators
excimer laser optics
target manipulators
pyrometer
casing of RHEED screen and camera
operator tool
AFM/STM system
atomic oxygen source
Laser-Molecular Beam Epitaxy
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[1] R. Gross et al., SPIE Conf. Proc. Vol. 4058 (2000), pp. 278-294
[2] J. Klein, C. Höfener, L. Alff, and R.Gross, Supercond. Sci. Technol. 12, 1023 (1999).
[3] J. Klein, C. Höfener, L. Alff, and R.Gross, J. Magn. and Magn. Mat. 211, 9 (2000).
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SrTiO3
La2/3Ba1/3MnO3
Oxide Heterostructures for Oxide Electronics
Example: Magnetic Tunnel Junction for
Magnetic Random Access Memories (MRAM)
SrTiO3
La2/3Ba1/3MnO3
La2/3Ba1/3MnO3
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Clean Room: 50m², class 100
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Electron Beam Lithography
Philips XL30 SFEG
Lithography System:
Raith ELPHY plus
2µm
Al
JJs
Al
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Intel dual-core 45 nm
(2007)
first transistor (1947)
Bardeen, Brattain, & Shockley
vacuum tubes
ENIAC (1946)
Enigma (1940)
physics
technology
superconducting Qubit
20 µm
WMI
From mechanical to quantum mechanical IP
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Collaborative Research Center 631 Cluster of Excellence NIM
CeNS
F
WSI
F
Semiconductor Quantum Dots
MPQ
Trapped Atoms and Ions
2 µm
Al
WMI
Superconducting Qubits
Development of Hardware Platform for QIP Systems
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Superconducting Quantum Devices and Circuits
Flux Qubit
coplanar waveguide resonator 1.25 GHz
Q > 105
hybrid ring S23 = - 3 dB S31 = - 50 dB
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• minimum temperature ~20 mK • HF shielded room • silver box for HF-shielding • magnetic shielding: cryoperm and
double µ-metal shielding • low temperature low-pass filter (GHz) • room temperature low-pass filter
experimental setup for qubit characterization
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Low temperature scanning probe techniques
Omicron 5K-UHV-STM
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„Dry“ dilution refrigerator (~ 20 mK)
commercial exploitation by Vericold GmbH, Ismaning
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27
innovative cryoengineering
…..WMI develops first dry dilution fridge
K. Uhlig, Cryogenics 42, 73 – 77 (2002)
Oxford Instruments Triton family
market share of dry dilution fridges: > 90%
„Dry“ dilution refrigerator (~ 20 mK)
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WMI Quantum Science Laboratory
Dezember 2011
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New mK Facilities for Circuit-QED Experiments
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Helium-Liquefaction
• Helium liquefier at WMI: Linde TCF 20
• supply of LHe to both Munich Universities
• liquefaction power: > 150 000 l/year
• market price: about 1 Mio. €
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Some Introductory
Remarks
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Temperature Scale
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
tem
per
atu
re (
K)
same amount of new physics on every decade of log T scale
center of hottest stars
center of the sun, nuclear energies
electronic energies, chemical bonding
surface of sun, highest boiling temperatures
organic life
liquid air
liquid 4He universe
superfluid 3He
lowest temperatures of condensed matter
elec
tro
nic
m
ag
net
ism
nu
clea
r-
ma
gn
etis
m
sup
erco
nd
uct
ivit
y
low
te
mp
era
ture
re
se
arc
h
lowest temperature in nuclear spin system achieved by adiabatic demagnetization of Rhodium nuclei: ≈ 100 pK
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Year
low
tem
per
atu
res
ult
ra-l
ow
tem
per
atu
res
paramagnetic refrigeration
nuclear demagnetization
Generation of Low Temperatures - History
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Carl Paul Gottfried von Linde * 11. Juni 1842 in Berndorf, Oberfranken
† 16. November 1934 in Munich
Low Temperature Technology in Germany
1868 offer of chair at the Polytechnische Schule München (now TUM)
1873 development of cooling machine allowing the temperature stabilization in beer brewing
21. 6. 1879 foundation of „Gesellschaft für Linde’s Eismaschinen AG“ together with two beer brewers and three other co-founders
1892 - 1910 re-establishment of professorship
12.5.1903 patent application: „Lindesches Gegenstrom- verfahren“ liquefaction of oxygen (-182°C = 90 K)
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Walther Meißner * 16. Dezember 1882 in Berlin
† 15. November 1974 in Munich
1913 – 1934 building and heading of low temperature laboratory at the Physikalisch-Technischen- Reichsanstalt, liquefaction of H2 (20K)
7.3.1925 first liquefaction of He in Germany (4.2 K, 200 ml), 3rd system world-wide besides Leiden and Toronto
1933 discovery of perfect diamagnetism of superconductors together with Ochsenfeld Meißner-Ochsenfeld Effect
1934 offer of chair at the Technische Hochschule München (now TUM)
1946 – 1950 president of the Bayerischen Akademie der Wissenschaften
1946 foundation of the commission for Low Temperature Research Walther-Meißner-Institut
Walther Meißner - der Mann, mit dem die Kälte kam W. Buck, D. Einzel, R. Gross, Physik Journal, Mai 2013
Low Temperature Technology in Germany